# Spectral resolution

The spectral resolution or resolving power of a spectrograph, or, more generally, of a frequency spectrum, is a measure of its power to resolve features in the electromagnetic spectrum. It is usually defined by

$R = {\lambda\over\Delta\lambda}$

where $\Delta\lambda$ is the smallest difference in wavelengths that can be distinguished, at a wavelength of $\lambda$. For example, the Space Telescope Imaging Spectrograph (STIS) can distinguish features 0.17 nm apart at a wavelength of 1000 nm, giving it a resolving power of about 5,900. An example of a high resolution spectrograph is the Cryogenic High-Resolution IR Echelle Spectrograph (CRIRES) installed at ESO's Very Large Telescope, which has a spectral resolution of up to 100,000[1].

The spectral resolution can also be expressed in terms of physical quantities, such as velocity; then it describes the difference between velocities $\Delta v$ that can be distinguished through the Doppler effect. Then, the definition is

$R = {c\over\Delta v}$

where $c$ is the speed of light. The STIS example above then has a spectral resolution of 51 km/s.

## References

1. Kim Quijano, J., et al. (2003), STIS Instrument Handbook, Version 7.0, (Baltimore: STScI)